Michelle Williams may win an Oscar for her portrayal of Marilyn Monroe, who was snubbed by the Academy. Dougray Scott plays Arthur Miller.

Brilliantly playing doomed ’50s sex bomb Marilyn Monroe, Michelle Williams gets under the skin of the troubled yet vulnerable icon in a way no one else ever has.

Her extraordinary performance in “My Week With Marilyn” makes all of the many performers who have played Monroe previously seem like cheap imitators — and lends gravitas to a lightweight romantic fantasy that dubiously claims to be based on fact.

In a tour de force, Williams subtly deploys her voice and body to effectively play three parts. In addition to a Marilyn who publicly flirts with reporters and young male fans, there’s the insecure diva who wreaks havoc on an English movie set in 1956 — enraging her haughty director and co-star, acting legend Sir Laurence Olivier (a hilarious Kenneth Branagh).

Williams also toggles into the co-title role in the famously troubled movie they’re making, the period romantic farce “The Prince and the Showgirl” (herein referred to by its working title, “The Sleeping Prince”).

When Marilyn’s distant and frustrated new husband Arthur Miller (Dougray Scott) abruptly leaves for a visit to the United States, Marilyn — perennially late and often forgetting lines in a fog of pills and booze — stops showing up for work altogether.

According to a widely disputed 2000 memoir by Clark — son of famed art historian Sir Kenneth Clark, a longtime friend of Olivier and his wife Vivien Leigh (Julia Ormond) — on which the film is partly based, this led to a daylong outing together, and two nights spent (chastely) in her bed.

Whether or not if you buy this as actually true — I don’t — these scenes are the most charming in the film. At one point, Marilyn, then 30, talks Colin into skinny-dipping with her in the Thames, remarking, “This is the first time I’ve ever kissed anybody younger than me.”

There’s also a visit to Colin’s school, Eton, as well as a Windsor Castle tour conducted for the wide-eyed Marilyn by the royal librarian (Derek Jacobi), who just happens to be Colin’s godfather.

Indeed, one of the film’s most magical moments comes at their departure, when Marilyn turns to Colin and whispers, “Shall I be ‘her’?” before sashaying in front of a delighted group of employees.

Following this escapade, Colin is sternly warned to stay away from Marilyn by her business partner Milton Greene (Dominic Cooper), a pill-dispensing ex-lover whose life savings are tied up in “The Prince and the Showgirl,” the first and only film from Marilyn Monroe Productions.

Somehow it’s young Colin who Greene urgently summons when a distraught Marilyn locks herself in a bathroom following a miscarriage.

Despite such darker moments that seem ripped from the pages of dozens of Monroe biographies, “My Week With Marilyn” maintains a remarkably breezy tone for much of its brisk length, thanks to Simon Curtis, a British TV director making his theatrical debut.

Judi Dench appears as the veteran actress Dame Sybil Thorn-dike, who encourages Marilyn on the set — and chastises the aging Olivier, who is jealous of her magical on-screen presence.